Fibonacci Series

 Fibonacci sequence

These numbers can be appreciated in many different ways. From the standpoint of calculation, they are as easy to understand as 0 + 1 which is 1, 1 +1 which is 2, 1+2 which is 3, and so on

0 1 1 2 3 5 8 13 21 34 55 89…….. (Fibonacci sequence)

(0+1 =1), (1+1 =2), (1+2 =3), (2+3 =5), (3+5=8), (5+8 =13), (8+13 =21), (13+21 =34), (21+34 =55), (34+55 =89)…

13				21
3	2		8
	1	1
5

 

A young Italian mathematician named Leonardo da Pisa — no relation to da Vinci —, 1202, published a book titled Liber Abaci. That's Latin for "Book of Calculation." These numbers appeared in his book which taught the Western countries the methods of arithmetic that we use today often.

In terms of application Fibonacci numbers appear in nature. For example, the number of petals on a flower or the number of spirals on a sunflower or a pineapple tends to be Fibonacci numbers.

It has beautiful number patterns. Suppose you like to square the first few numbers of Fibonacci

0²       1²     1²      2²      3²     5²     8²     13²       21²       34²      55²…….. 

0        1       1       4        9      25     64    169      441     1156    3025…….

When you add consecutive Fibonacci square numbers value together you can see that the patterns continue from the normal Fibonacci sequences. For example,

(1+1 =2), (1+4 = 5), (4+9 =13)…..

And if you divide the larger number by the smaller number, you get a ratio of around 1.618. This number is known as Golden Ratio

So how is it used in today’s world? It is mainly used in hashing and hash tables.